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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

4 votes
1 answer
473 views

CLT convergence rate for sum of uniforms (in TV distance)

Suppose $X_1, \cdots, X_n \sim_{\mathrm{iid}} U([-1,1])$, where $U([-1, 1])$ denotes the continuous uniform distribution over the interval $[-1, 1]$ (so $E[X_i] = 0$ and $\text{Var}[X_i]= 1/3$). Let $ …
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80 views

High probability bound on number of sparse solutions to Gaussian linear system

Suppose we have a random matrix $A \in \mathbb{R}^{m \times n}$ with all entries i.i.d. from the standard Normal distribution $\mathcal{N}(0, 1)$. Suppose $k$ divides $n$, and let $S \subseteq \mathbb …
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